This paper investigates polygonal approximation in boundary representation for two-dimensional objects using an ant colony algorithm. Ant colony algorithm is a newly optimization algorithm for the field of stochastic researching recently. In the proposed approach, in according with the pheromone strength and the arc-to-chord distance for a curve, we construct an optimizing Ant Colony Algorithm (ACA) that based on the ability of ants to find the optimal dominant points in a curve between the source and destination. The experimental results show that the proposed ACA with the roulette wheel selection can obtain better performance than that generated by the conventional polygonal approximation methods.